By Christmas of 1776, the Revolution was in a sorry state. With superior training, numbers, and naval capability, the British had overwhelmed the Continental Army in battle after battle from Long Island, south through New Jersey, finally driving them across the Delaware River, just north of the rebel capital of Philadelphia, on Dec 8.

General Washington had the strategic sense to order as many boats as possible to the Delaware's west bank, in the course of retreat; this alone had prevented the British from sweeping directly to Philly. His troops were ill-equipped, undersupplied, and inexperienced. Many lacked shoes. Civilian support was still rather evenly divided between the British and the fledgling Continental Congress; and there was no aid forthcoming from abroad (yet).

Time was against Washington. The Delaware would soon freeze over completely, permitting a leisurely invasion of the First Capital. New Year's Day would also would mark the expiration of his troops' terms of enlistment; the harsh conditions, poor provisioning, and depressing string of strategic losses were already taking a heavy toll of desertion. After dark on Christmas Day, aided by Massachusetts boatsmen under Colonel John Glover, some 2400 troops were ferried back to the eastern shore. They were beset with blinding snow and hail, which detained additional supporting troops (led by Generals Thomas Cadwalader and James Ewing), and the Delaware itself was awash with treacherous ice floes. In the wee hours of December 26, the Continental troops marched on Trenton. Their victory at the First Battle of Trenton would go a long way toward lifting morale, and maintaining a safer buffer between the British army and Philadelphia for the winter. Also, it increased foreign confidence in the revolutionaries' capability, which would result in support and aid from France. Finally, captured Hessian mercenaries would prove valuable trainers for the ragtag militia.

Leutze's interpretation is as inaccurate as it is symbolic. The sky suggests dawn, but the actual crossing was completed well before first light. The flag design shown wouldn't be approved by Congress until June 14, 1777; the flag in use at the time would have been the "Grand Union" design, with a Union Jack in place of the circle of stars. Washington, shown standing, would have risked being pitched into the icy Delaware; he was more likely seated or catching some shut-eye. Oddly, the shading effect on the faces of the oarsmen suggests conflicting light sources. (These are the most glaring inaccuracies, there are others.)

Sources:"George Washington Crossing the Delaware - The Metropolitan Museum of Art", http://www.metmuseum.org/explore/gw/el_gw.htm, The Metropolitan Museum of Art, 2000.
A good high-res image of the painting can be viewed at this URL.